True deterministic chaos is characterized by unpredictable, apparently random motion in a dynamical system completely described by a deterministic dynamic law, usually a nonlinear differential equation, with no stochastic component. The inability to predict future behavior of a chaotic system occurs because trajectories evolving from arbitrarily close initial conditions diverge. Chaos is universal as it may arise in any system governed by one of a class of quite common, suitable nonlinear dynamic laws. This book discusses both the experimental observation and theoretical interpretation of chaos in chemical and biochemical systems. Examples are drawn from the Belousov-Zhabotinsky reaction, surface reactions, electrochemical reactions, enzyme reactions, and periodically perturbed oscillating systems.

True deterministic chaos is characterized by unpredictable, apparently random motion in a dynamical system completely described by a deterministic dynamic law, usually a nonlinear differential equation, with no stochastic component. The inability to predict future behavior of a chaotic system occurs because trajectories evolving from arbitrarily close initial conditions diverge. Chaos is universal as it may arise in any system governed by one of a class of quite common, suitable nonlinear dynamic laws. This book discusses both the experimental observation and theoretical interpretation of chaos in chemical and biochemical systems. Examples are drawn from the Belousov-Zhabotinsky reaction, surface reactions, electrochemical reactions, enzyme reactions, and periodically perturbed oscillating systems.

Just a few decades ago, chemical oscillations were thought to be exotic reactions of only theoretical interest. Now known to govern an array of physical and biological processes, including the regulation of the heart, these oscillations are being studied by a diverse group across the sciences. This book is the first introduction to nonlinear chemical dynamics written specifically for chemists. It covers oscillating reactions, chaos, and chemical pattern formation, and includes numerous practical suggestions on reactor design, data analysis, and computer simulations. Assuming only an undergraduate knowledge of chemistry, the book is an ideal starting point for research in the field. The book begins with a brief history of nonlinear chemical dynamics and a review of the basic mathematics and chemistry. The authors then provide an extensive overview of nonlinear dynamics, starting with the flow reactor and moving on to a detailed discussion of chemical oscillators. Throughout the authors emphasize the chemical mechanistic basis for self-organization. The overview is followed by a series of chapters on more advanced topics, including complex oscillations, biological systems, polymers, interactions between fields and waves, and Turing patterns. Underscoring the hands-on nature of the material, the book concludes with a series of classroom-tested demonstrations and experiments appropriate for an undergraduate laboratory.

"This volume is a collection of the papers presented at the International Conference on Fractal Concepts and the Application of Chaos in Chemical Engineering Problems. The book provides a detailed description of the current research on the application of fractal concepts, nonlinear dynamics and disordered systems in chemical engineering, with emphasis on interdisciplinary connections with related fields, such as control theory of nonlinear systems, dynamic theory of fractals, transport theory and physical chemistry of heterogeneous materials."--Publisher's website.

Seventy years ago, Erwin Schrödinger posed a profound question: 'What is life, and how did it emerge from non-life?' This problem has puzzled biologists and physical scientists ever since. Living things are hugely complex and have unique properties, such as self-maintenance and apparently purposeful behaviour which we do not see in inert matter. So how does chemistry give rise to biology? What could have led the first replicating molecules up such a path? Now, developments in the emerging field of 'systems chemistry' are unlocking the problem. Addy Pross shows how the different kind of stability that operates among replicating molecules results in a tendency for chemical systems to become more complex and acquire the properties of life. Strikingly, he demonstrates that Darwinian evolution is the biological expression of a deeper, well-defined chemical concept: the whole story from replicating molecules to complex life is one continuous process governed by an underlying physical principle. The gulf between biology and the physical sciences is finally becoming bridged. This new edition includes an Epilogue describing developments in the concepts of fundamental forms of stability discussed in the book, and their profound implications. Oxford Landmark Science books are 'must-read' classics of modern science writing which have crystallized big ideas, and shaped the way we think.

Life, Hoffman argues, emerges from the random motions of atoms filtered through the sophisticated structures of our evolved machinery. People are essentially giant assemblies of interacting nanoscale machines.

This book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc.A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van der Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diods, stabilization of swings in power systems, increasing predictability of business-cycles are also presented.The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West.Researchers, teachers and graduate students in the fields of electrical and mechanical engineering, physics, chemistry, biology, economics will find this book most useful. Applied mathematicians and control engineers from various fields of technology dealing with complex oscillatory systems will also benefit from it.

In recent years experimental and numerical studies have shown that chaos is a widespread phenomenon throughout the biological hierarchy ranging from simple enzyme reactions to ecosystems. Although a coherent picture of the fundamental mechanisms responsible for chaotic dynamics has started to appear it is not yet clear what the implications of such dynamics are for biological systems in general. In some systems it appears that chaotic dynamics are associated with a pathological condi tion. In other systems the pathological condition has regular periodic dynamics whilst the normal non-pathological condition has chaotic dyna mics. Since chaotic behaviour is so ubiquitous in nature and since the phenomenon raises some fundamental questions about its implications for biology it seemed timely to organize an interdisciplinary meeting at which leading scientists could meet to exchange ideas, to evaluate the current state of the field and to stipulate the guidelines along which future research should be directed. The present volume contains the contributions to the NATO Advanced Research Workshop on "Chaos in Biological Systems" held at Dyffryn House, St. Nicholas, Cardiff, U. K. , December 8-12, 1986. At this meeting 38 researchers with highly different backgrounds met to present their latest results through lectures and posters and to discuss the applica tions of non-linear techniques to problems of common interest. . In spite of their involvement in the study of chaotic dynamics for several years many of the participants met here for the first time.

This book addresses the molecular bases of some of the most important biochemical rhythms known at the cellular level. The approach rests on the analysis of theoretical models closely related to experimental observations. Among the main rhythms considered are glycolytic oscillations observed in yeast and muscle, oscillations of cyclic AMP in Dictyostelium amoebae, intracellular calcium oscillation observed in a variety of cell types, the mitotic oscillator that drives the cell division cycle in eukaryotes, pulsatile hormone signaling, and circadian rhythms in Drosophila. This book will be of interest to life scientists such as biochemists, cell biologists, chronobiologists, medical scientists and pharmacologists. In addition, it will appeal to scientists studying nonlinear phenomena, including oscillations and chaos, in chemistry, physics, mathematics and theoretical biology.

New transdisciplinary studies have been appearing not only in such established areas as biochemistry or social psychology; there are presently emerging inter-scientific fields such as sociobiology, econophysics and last but not least sociophysics. The latter is a renewed attempt to combine the latest natural and social science theories and come up with significant generalisations for both. Using the powerful physics metaphor as an inertial guidance system, sociophysics emphasises the underlying similarities between all systems. This new scientific hybrid is raising much controversy as well as revealing great promise; for this reason, it has been chosen to provide the core and focus for this book. The holistic scope of this book makes it an appropriate reference work in many courses, such as: Global Ecology; Evolutionary Biology; Macroeconomics; Sociological Theory; Philosophy of Social Science; Theoretical Physics; Thermodynamics; Macro-history; Behavioural Science; General Systems Theory; and Interdisciplinary Studies.